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A local fitting algorithm for converting planar curves to B-splines

Chongyang Deng, Xunnian Yang
2008 Computer Aided Geometric Design  
In this paper we present a local fitting algorithm for converting smooth planar curves to B-splines.  ...  Finally, the Bézier spline is merged into a C 2 continuous B-spline curve by subdivision and control points adjustment.  ...  This work is supported by NSFC (60673032, 60333010) and 973 program of China (2002CB312101).  ... 
doi:10.1016/j.cagd.2007.11.001 fatcat:fuwwgxt6znacrbzch3iu3klhvy

Optimization of Active Muscle Force–Length Models Using Least Squares Curve Fitting

Goran Abdulrahman Mohammed, Ming Hou
2016 IEEE Transactions on Biomedical Engineering  
The minimal set of coefficients is identified for each of these models to facilitate the least squares curve fitting.  ...  by using the least squares curve fitting method.  ...  Ward * for making the rabbit muscles experimental data available to this study. * Department of Radiology, University of California and Veterans Administration Medical Centers, 3350 La Jolla Village Drive  ... 
doi:10.1109/tbme.2015.2467169 pmid:26276984 fatcat:k4kvgom7lzacritasqqujqdv2a

Video Data Compression by Prossive Iterative Approximation

M. J. Ebadi, A. Ebrahimi
2020 International Journal of Interactive Multimedia and Artificial Intelligence  
In the present paper, the B-spline curve is used for reducing the entropy of video data.  ...  The Lossless video data compression is done through storing the B-spline curve control points (CPs) and the difference between fitted and original video data.  ...  LSPIA provides a set of fitting curves making adjustments of the CPs and leading to the given data points through least square (LS) fitting as the final curve.  ... 
doi:10.9781/ijimai.2020.12.002 fatcat:bxev7i2suzhjjicucl4slx274a

Quantitative Estimation of Missing Value Interpolation Methods for Suomi-NPP VIIRS/DNB Nighttime Light Monthly Composite Images

Junfu Fan, Peng Zhang, Jiahao Chen, Bo Li, Liusheng Han, Yuke Zhou
2020 IEEE Access  
In this paper, we employed least-squares line fitting (LSLF), least-squares quadratic polynomial fitting (LSQPF), least-squares cubic polynomial fitting (LSCPF), cubic spline interpolation (Spline), cubic  ...  Hermite interpolation (Hermite), cubic Bezier curve interpolation (Bezier), gray forecast model (GFM) and cubic exponential smoothing (Exponent) to simulate the missing values in VIIRS/DNB data.  ...  In this paper, eight commonly used algorithms, including least-squares line fitting (LSLF), least-squares quadratic polynomial fitting (LSQPF), least-squares cubic polynomials fitting (LSCPF), Spline,  ... 
doi:10.1109/access.2020.3035408 fatcat:g7scld6enrhtdpdyuzjqpurdse

Investigating the quality inspection process of offshore wind turbine blades using B-spline surfaces

Dominic Auger, Qing Wang, Jon Trevelyan, Songling Huang, Wei Zhao
2018 Measurement (London)  
W. (2018) 'Investigating the quality inspection process of oshore wind turbine blades using B-spline surfaces. ', Measurement., Additional information: Use policy The full-text may be used and/or reproduced  ...  The presented protocol was found to increase the fitness of a surface by up to 150%.  ...  ACKNOWLEDGMENT This research is part of the wind turbine structural condition monitoring program funded by EPSRC through the Centre for Through Life Engineering Services (EP/1033246/1, Project SC006) and  ... 
doi:10.1016/j.measurement.2017.10.027 fatcat:xkqz6llhmnctzc3bwdkz4lpeaa

A novel approach for computing C2-continuous offset of NURBS curves

S.-H.F. Chuang, J.-L. Shih
2006 The International Journal of Advanced Manufacturing Technology  
Based on the initial offset and a set of selected knots, an intended C 2 -continuous B-spline curve is subsequently constructed.  ...  The method uses a new error-measuring scheme, which is based on the convex hull property of Bézier curves and the idea of cumulative errors, to calculate the global error bound of offset approximation.  ...  C 2 -continuous piecewise Bézier curve and B-spline representation A number of Bézier curves can be joined end to end to form a piecewise Bézier curve (or a composite Bézier curve) [9] .  ... 
doi:10.1007/s00170-004-2484-x fatcat:g4mapv5jyzeknmwyzukb4i33sa

Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic Bézier Splines [article]

Martin Hanik and Hans-Christian Hege and Anaja Hennemuth and Christoph von Tycowicz
2020 arXiv   pre-print
We present a framework for nonlinear regression on manifolds by considering Riemannian splines, whose segments are B\'ezier curves, as trajectories.  ...  Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes.  ...  Right: A Bézier spline with 3 cubic segments on S 2 .Property (2) allows us to fit Bézier curves of possibly different orders together to a differentiable spline.  ... 
arXiv:2007.05275v2 fatcat:y3kztitorbcy7kfi6lfcxt3fce

Comparing offset curve approximation methods

G. Elber, In-Kwon Lee, Myung-Soo Kim
1997 IEEE Computer Graphics and Applications  
This divide and conquer approach exploits the subdivision property of the base curve C(t). Henceforth, we assume C(t) is represented by a Bézier or NURBS curve.  ...  : The error function (t) is obtained by symbolically computing the difference and inner product of Bézier or NURBS curves (see Sidebar on Symbolic Computation and Reference [8]).  ...  Several examples of Bézier and B-spline curves are given, both in polynomial and rational forms.  ... 
doi:10.1109/38.586019 fatcat:ihv5bch5zvc4deeutv7yzhxg4u

Page 253 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
For interpolation, we discuss macro- element methods and minimal energy splines, and for fitting, we consider discrete least squares and penalized least squares.”  ...  We obtain the best one- degree reduction of Bézier curves of degree n < 5 with endpoint interpolation by using perfect splines.  ... 

Post-processing and visualization techniques for isogeometric analysis results

Annette Stahl, Trond Kvamsdal, Christian Schellewald
2017 Computer Methods in Applied Mechanics and Engineering  
The presented post-processing and visualization techniques thereby strengthen the relation between geometry, analysis and visualization.  ...  This is achieved by facilitating the same mathematical function space used for geometry and analysis also for post-processing and visualization purposes.  ...  Acknowledgments The authors acknowledge the financial support from the Norwegian Research Council and the industrial partners of the ICADA-project (NFR Project 187993); Ceetron, Det Norske Veritas and  ... 
doi:10.1016/j.cma.2016.10.040 fatcat:if2uyoutlzhuxislqse2ujzvsy

Adaptive Smooth Scattered-data Approximation for Large-scale Terrain Visualization [article]

Martin Bertram, Xavier Tricoche, Hans Hagen
2003 EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization  
The scheme is memory efficient, easy to implement and produces smooth surfaces. It combines adaptive clustering based on quadtrees with piecewise polynomial least squares approximations.  ...  We present a fast method that adaptively approximates large-scale functional scattered data sets with hierarchical B-splines.  ...  Acknowledgements The Crater Lake and Seattle datasets used to test our method were provided by U.S. Geological Survey (USGS).  ... 
doi:10.2312/vissym/vissym03/177-184 fatcat:gswefpxe7zhh3fqjytrphs7jxy

Heterogeneous modeling of medical image data using B-spline functions

Olya Grove, Khairan Rajab, Les A Piegl
2012 Proceedings of the Institution of mechanical engineers. Part H, journal of engineering in medicine  
A special thank you to Catherine Burton for her support and willingness to help the students.  ...  Dr Piegl's guidance and support has been quintessential to my growth as a student and a researcher.  ...  Hence, least-squares Bezier fitting is applied to obtain a set of 0 C Bezier curves that approximate the data to within a tolerance.  ... 
doi:10.1177/0954411912452995 pmid:23157075 fatcat:fhg2zep6mvgedjolc3uc4zuizy

Page 9500 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Summary: “A least squares approximation by tensor products of B-splines for large sets of scattered data is considered.  ...  These curves possess the properties of Bézier curves and B- spline curves. In addition, as a — 0, they approach respectively the quartic Bézier curves and quartic B-spline curves.  ... 

Curve Watermarking Technique for Fingerprinting Digital Maps

Yongjian Hu, Heung-Kyu Lee, Huafei Zeng
2008 2008 International Conference on Intelligent Information Hiding and Multimedia Signal Processing  
Curves are one of the major components of digital maps. In order to fingerprint digital maps, this paper addresses an efficient watermarking technique for curves.  ...  The watermarked curve is reconstructed using Bezier curve segments. The use of Bezier model ensures not only large embedding capacity and high detection response but also small embedding distortion.  ...  Bezier curves can be written as ) ( ) ( , 0 t B P t P n i n i i ¦ (1) where P i refers to the control point, and BB i,n (t) is the weight of the ith control point and known as the nth order Bezier blending  ... 
doi:10.1109/iih-msp.2008.159 dblp:conf/iih-msp/HuLZ08 fatcat:yjw2hmkufvayxiozymztxagmw4

Page 3573 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
Tambulea, Generalizations of Bézier curves and surfaces (169-176); M. Gasca and J. M. Pena, Corner cutting algorithms and totally positive matrices (177-184); S.  ...  Josef Hoschek and Franz-Josef Schneider, Approximate conver- sion and data compression of integral and rational B-spline sur- faces (241-250); B. Jiittler and R.  ... 
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